Question: Rewrite as a simplified fraction. ${3.\overline{15} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 315.1515...\\ 1x &= 3.1515...\end{align*}}$ Subtracting the two equations, we have: ${99x = 312}$ ${x = \dfrac{312}{99}} $ ${x = \dfrac{104}{33}} \text{or} {3 \dfrac{5}{33}}$